Method of Separable Variables Q8

Method of Separable Variables Q8

Find the general solution of the differential equation
\((x^{2}+1)\frac{\mathrm{d}y}{\mathrm{d}x}=y-1\),
expressing \(y\) in terms of \(x\).

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Answer:\(y=Ae^{\tan^{-1}x}+1,\quad A\in\mathbb{R}\)

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